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Proof step 24 from proof unmodified-payload (previous step)

BRANCH_SIZE = # zbrar, iast[adr] = indexnode(save(zbrar, 0, nused), bv1, nused), zbrar[n] = mkzentry(zbrar[n0].key, adr0), zbrar[n0].entry?, n0 + 1 < BRANCH_SIZE, n0 + 1 < nused, n < nused, n < BRANCH_SIZE, n0 < n, n0 < nused, n0 < BRANCH_SIZE, sorted(zbrar, 0, nused), zbrar[n0].key ∈ payload(zbrar, 0, nused), adr ∈ iast, nused ≤ BRANCH_SIZE, ∀ n1. n1 < n ∧ zbrar[n1].entry? → zbrar[n1].key ≠ zbrar[n0].key ⊦ payload(zbrar, 0, nused)[zbrar[n0].key] = adr0

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: zbranch name: elim-03 seq: ⊦ zbr.entry? → (key = zbr.key ∧ adr = zbr.adr ↔ zbr = mkzentry(key, adr)) subst: [zbr, key, adr] → [zbrar[n0], key, adr1]

Additional information

Used simplifier rules: m0 < m, m1 < m, m ≤ # zbrar ⊦ sorted(zbrar, 0, m) ∧ zbrar[m0] = mkzentry(key, adr0) → (zbrar[m1] = mkzentry(key, adr1) ↔ m0 = m1 ∧ adr0 = adr1); (ws)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → ¬ n < m; (s)%⊦ zbr.entry? → (key = zbr.key ∧ adr = zbr.adr ↔ zbr = mkzentry(key, adr)); (elim) Used terms: zbrar[n0], key, adr1